Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity

TL;DR

This paper investigates how modified gravity theories, specifically $f(R)$ gravity, influence the size of black hole shadows and photon spheres, inspired by recent astrophysical observations of supermassive black holes.

Contribution

It introduces the effects of $f(R)$ modified gravity on black hole photon spheres and shadows, highlighting the role of a new scalar degree of freedom $F$ in these phenomena.

Findings

Signature of modified gravity on photon sphere size

Alterations in black hole shadow due to $f(R)$ theory

Influence of scalar degree of freedom $F$ on observable features

Abstract

Black hole shadows are a widespread topic in astrophysics. This paper searches for an optical view of the black hole and the relationship between black hole shadow and photon sphere with curvature. We were inspired by the observations of Sagittarius $A^*$ and supermassive black hole M87$*$ through the Event Horizon Telescope. We have found the signature of the modified theory of gravity on the photon sphere and shadow. We considered $f(R)$ modified theory of gravity and new scalar degree of freedom $F$ appears in the expressions of photon sphere and shadow.